Simultaneous inorganic, organic and byproduct analysis in electrochemical deposition solutions

ABSTRACT

Real-time analysis of electrochemical deposition (ECD) metal plating solutions is described, for the purpose of reducing plating defects and achieving high quality metal deposition. Improved plating protocols are utilized for increasing potential signal strength and reducing the time required for each measurement cycle. New methods and algorithms for simultaneously determining concentrations of organic additives, inorganic additives, and/or byproducts in a sample ECD solution are described. In one aspect, a method is provided for simultaneously determining concentrations of all organic additives, inorganic additives, and/or byproducts within a single experimental run by using a single analytical cell, while interactions between such additives are properly accounted for.

CROSS-REFERENCE TO RELATED APPLICATION

The benefit of priority of U.S. provisional patent application60/764,614 filed Feb. 2, 2006 in the names of Jianwen Han, et al. for“SIMULTANEOUS INORGANIC, ORGANIC AND BYPRODUCT ANALYSIS INELECTROCHEMICAL DEPOSITION SOLUTIONS,” is hereby claimed under theprovisions of 35 USC 119. The disclosure of such U.S. provisional patentapplication is hereby incorporated herein by reference in its entirety,for all purposes.

FIELD OF THE INVENTION

This invention relates generally to methods and apparatuses formonitoring organic and inorganic additives as well as byproductconcentrations in electrochemical copper plating baths, preferably usinga single analysis system.

BACKGROUND OF THE INVENTION

In the practice of copper interconnect technology in semiconductormanufacturing, electrochemical deposition (ECD) is widely employed forforming copper interconnect structures on microelectronic substrates.The Damascene process, for example, uses physical vapor deposition todeposit a seed layer of copper on a barrier layer, followed byelectrochemical deposition of copper.

In the ECD operation, organic additives as well as inorganic additivesare employed in the plating solution in which the metal deposition iscarried out. The ECD process is sensitive to concentration changes oforganic, inorganic and, as disclosed herein, byproduct components. Sinceconcentrations of bath components can vary considerably as they areconsumed and/or produced during the life of the bath, it therefore isdesirable to conduct real-time monitoring and replenishment of all majorbath components to ensure optimal process efficiency and yield of thesemiconductor product incorporating the electrodeposited copper.

Presently, inorganic and organic additives of the copper ECD baths areanalyzed using separate analysis systems, none of which are capable ofquantifying byproducts. For example, inorganic components of the copperECD bath, including copper, sulfuric acid and chloride, conventionallyare measured by potentiometric analysis. Organic additives such assuppressors, accelerators, and levelers are added to the ECD bath tocontrol uniformity of the film thickness across the wafer surface. Theconcentration of the organic additives can be measured by pulsed cyclicgalvanostatic analysis (PCGA), which mimics the plating conditionsoccurring on the wafer surface. In the practice of the PCGA method,copper is electroplated onto a working or testing electrode, bysupplying a sufficient current (or potential), while monitoring thecorresponding potential (or current). The electrical potential (orcurrent) measured during such electroplating step correlates with theorganic additive concentrations in the sample electroplating bath, andtherefore can be used for determining concentrations of organicadditives. For further details regarding the PCGA processes, please seeU.S. Pat. No. 6,280,602 issued Aug. 28, 2001 to Peter M. Robertson for“Method and Apparatus for Determination of Additives in Metal PlatingBaths,” the disclosure of which hereby is incorporated herein byreference for all purposes.

There are several implications associated with said separate analysesincluding, but not limited to:

-   -   (1) more sample must be used for two or three separate analyses;    -   (2) multiple analyzers equates to a larger expense upfront,        larger maintenance costs and a larger overall footprint;    -   (3) if byproduct(s) cannot be detected then “bleed and feed”        schemes cannot be optimized nor can defects on wafers be        predicted as a function of foreign bath material.

Accordingly, there is a continuing need to improve the PCGA analysis oforganic additives in ECD baths and to provide more stable analyticalsignals and reduce noise and measurement errors.

There is also a need to expand the improved PCGA process so thatinorganic and byproduct species present in the ECD baths may be analyzedand quantified using the same analysis system.

There is a further need to modify the conventional PCGA procedures toachieve shorter calibration and measurement cycles, reduce the analysistime, and simplify the hardware and software required for performing thePCGA analysis.

There is still a further need to account for interactions between thedifferent types of ECD additives and their byproducts and their impacton the PCGA analysis results.

Other objects and advantages will be more fully apparent from theensuring disclosure and appended claims.

SUMMARY OF THE INVENTION

The present invention relates generally to real-time analysis of ECDmetal plating solutions, for the purpose of reducing plating defects andachieving high quality metal deposition, and systems for performing suchanalysis.

One aspect of the present invention relates to methods of analyzingcopper ECD bath compositions comprising measuring ECD bath byproductsand, optionally, measuring organic additives and/or inorganic additivesin said bath compositions, wherein said measuring is preferablyperformed using a single analysis system and/or a single bath sample.Most preferably, a single sample of the bath composition is measuredusing a single analysis system.

Another aspect of the present invention relates to methods of analyzingcopper ECD bath compositions comprising measuring ECD bath byproducts,organic additives and inorganic additives. One preferred embodimentrelates to methods comprising performing said measuring using a singleanalysis system and/or a single sample. Most preferably, a single sampleof the bath composition is measured using a single analysis system.

Another aspect of the invention relates to a method forelectrochemically determining the concentration of one or more targetcomponents in a sample electrochemical deposition solution, comprisingthe steps of:

-   -   (a) contacting a working electrode and a counter electrode with        the sample electrochemical deposition solution;    -   (b) applying a potential pulse between the working and counter        electrodes for a sufficient period of time to induce metal        nucleation on an surface of the working electrode;    -   (c) subsequently, applying a constant plating current between        the working and counter electrodes sufficient for effectuating        electrochemical deposition of metal onto the surface of the        working electrode from the sample electrochemical deposition        solution;    -   (d) monitoring potential response of the sample electrochemical        deposition solution under the constant plating current; and    -   (e) determining concentration of one or more target components        in such sample electrochemical deposition solution, based on the        potential response of the sample electrochemical deposition        solution measured under the constant plating current.

Preferably, such sample electrochemical deposition solution is a copperelectroplating solution that comprises copper sulfate, sulfuric acid,chloride, and one or more organic additives such as suppressors,accelerators, and levelers, while the target components forconcentration analysis are the one or more organic additives, one ormore inorganic additives, and/or byproducts of said additives.Preferably, the measuring is performed using a single analysis systemand/or a single sample. Most preferably, a single sample of the bathcomposition is measured using a single analysis system.

Another aspect of the present invention relates to a method forconducting electrochemical analysis of a sample electrochemicaldeposition solution, said method comprising the steps of providing ameasurement chamber having a measuring electrode, a counter electrode,and a reference electrode therein, and performing in such measurementchamber one or more measurement cycles by using said sampleelectrochemical deposition solution. Each of such measurement cyclescomprises the sequential steps of:

-   -   (a) electrostripping the measuring electrode to remove metal        residue formed thereon during a previous measurement cycle;    -   (b) applying a cyclic electropotential between the measuring and        counter electrodes to remove organic residue formed on the        measuring electrode during a previous measurement cycle;    -   (c) filling the measurement chamber with fresh sample        electrochemical deposition solution and allowing the measuring        electrode and counter electrode to reach an equilibrium state in        the sample solution;    -   (d) electrochemically depositing metal onto the measuring        electrode by applying a constant electrical current between the        measuring electrode and counter electrode through the sample        electrochemical deposition solution, while concurrently        monitoring potential response of the sample solution; and    -   (e) applying an electropotential between the measuring electrode        and counter electrode to remove at least a part of the metal        deposit formed on the measuring electrode.

Preferably, the sample electrochemical deposition solution is a copperelectroplating solution that comprises copper sulfate, sulfuric acid,chloride, and one or more organic additives such as suppressors,accelerators, and levelers. Preferably, the analysis measures theconcentration of the one or more organic additives, one or moreinorganic additives, and/or byproducts of said additives. Morepreferably, the measuring is performed using a single analysis systemand/or using a single sample, most preferably simultaneously using asingle analysis system and/or using a single sample.

An electrolytic cleaning solution comprising sulfuric acid can be usedfor electrostripping in step (a). More preferably, a portion of theelectrostripping is conducted while such electrolytic cleaning solutionis flushed through the measurement chamber, to remove metal residuesthat have been stripped off the measuring electrode and avoid furthercontamination of the measurement chamber by such metal residues.

Such electrolytic cleaning solution may also be used to flush themeasurement chamber when the cyclic electropotential is applied betweenthe measuring and counter electrodes (i.e., cyclic voltammetry or CVscan) in step (b), to remove organic residues that come off theelectrode surface during the CV scan.

The equilibrium state in step (c) may be reached by disconnecting themeasuring electrode from the counter electrode, to form an open circuit.Alternatively, such equilibrium state can be reached by applying apredetermined electropotential that is less than the copper platingpotential between the measuring electrode and the counter electrode.

The electroplating in step (d) is preferably preceded by a potentialpulse of from about −0.1V to about −1V, to facilitate formation of metalnuclei on the electrode surface, and followed by a strippingelectropotential of from about 0.1V to about 0.5V, to remove at least apart of the metal plate formed during step (d) and thereby reduce therisk of alloying between such metal plate and metal component of themeasuring electrode.

Still another aspect of the present invention relates to a method forsimultaneously determining concentrations of copper sulfate, sulfuricacid, chloride ion, suppressor, accelerator, leveler, and/orbyproduct(s) thereof in a sample electrochemical deposition solution,comprising the steps of:

-   -   (a) identifying one or more non-compositional variables that        affect electropotential responses of electrochemical deposition        solutions during electrochemical metal deposition;    -   (b) establishing a multiple regression model that expresses the        electropotential responses of electrochemical deposition        solutions as a function of (1) said one or more        non-compositional variables, (2) organic additive concentrations        in the solutions, (3) inorganic additive concentrations in the        solutions, (4) byproduct concentrations in the solutions, and        the corresponding coefficients;    -   (c) conducting multiple calibration runs, by measuring        electropotential responses of multiple calibration solutions        having unique, known organic additive, inorganic additive,        and/or byproduct concentrations at unique, predetermined values        of said one or more variables;    -   (d) determining the coefficients that correspond to said one or        more variables and the organic additive, inorganic additive,        and/or byproduct concentrations in the multiple regression        model, based on information obtained from the calibration runs;        and    -   (e) conducting N experimental runs, by measuring        electropotential responses of the sample electrochemical        deposition solution at unique, predetermined values of said one        or more variables;    -   (f) establishing N number of equations based on the established        multiple regression model, said equations containing the        coefficients determined in step (d), the electropotential        responses measured during the N experimental runs in step (e)        and the corresponding predetermined values of said one or more        variables, and the unknown concentrations of the copper sulfate,        sulfuric acid, chloride ion, suppressor, accelerator, leveler,        and/or byproduct(s) thereof in the sample electrochemical        deposition solution; and    -   (g) calculating said copper sulfate, sulfuric acid, chloride        ion, suppressor, accelerator, leveler, and/or byproduct        concentrations in the sample solution by solving the N equations        provided in step (f),        wherein N corresponds to the total number of organic additive,        inorganic additive and/or byproduct species simultaneously        quantified using such method.

Preferably, analysis of variance is used for identifying thenon-composition variables that have significant impact on theelectropotential responses of the electrochemical deposition solutions.Specifically, a preliminary multiple regression model including termsfor all non-compositional variables that have potential impact on theelectropotential responses is constructed, and analysis of variancetests are carried out to (1) estimate the parameters or coefficientsassociated with such variables and (2) determine the probability orlikelihood that such coefficients are equal to zero. Only thosevariables having non-zero coefficients at confidence levels of not lessthan 95% (i.e., the probability of such coefficients being zero is notmore than 5%) are selected to be included into a multiple regressionmodel for determination of the organic additive, inorganic additiveand/or byproduct concentrations.

Six (6) non-composition variables have been identified using suchanalysis of variance tests for analysis of organic additive, inorganicadditive and/or byproduct concentration in copper electroplatingsolutions, which include (1) nucleation potential (i.e., the potentialpulse before current plating); (2) nucleation time, (3) electroplatingcurrent, (4) electroplating time, (5) scan rate (i.e., potential changerate) of the cyclic voltammetry during pre-plating cleaning process, (6)size of the measuring electrode used during the electrochemicalanalysis, and (7) temperature.

A multiple regression model including terms for these selectednon-compositional variables and for the organic additive, inorganicadditive and/or byproduct concentrations is then established in step(b). An important advantage of the method of the present invention isthat it provides terms to account for interactions between thenon-compositional variables and/or the additive (and/or byproduct)concentrations.

Once all the coefficients for the non-compositional variables and theadditive (and/or byproduct) concentrations in such multiple regressionmodel are determined via calibration, the actual sample analysis startsby conducting N experimental runs, each of which has a different sets ofpredetermined values for the non-compositional variables. As definedherein, “N” corresponds to the total number of species being quantified,wherein the species may include organic additives, inorganic additives,and/or byproducts thereof. The electroplating potentials of the sampleelectrochemical deposition solution in such N experimental runs aremeasured and used to establish N number of equations according to theestablished multiple regression model. Each equation contains knowncoefficients, known values of the non-compositional variables, and theelectroplating potential value as measured. The only N unknown values insuch equations are the organic additive, inorganic additive and/orbyproduct concentrations, which can be readily determined by solving theN number of equations.

The N experimental runs can be conducted sequentially in a singleelectrochemical analytical cell. Alternatively, they can be carried outsimultaneously in N electrochemical analytic cells having N differentplating protocols or settings.

A further aspect of the present invention relates to a method forsimultaneously determining concentrations of copper sulfate, sulfuricacid, chloride ion, suppressor, accelerator, leveler, and/orbyproduct(s) thereof in a sample electrochemical deposition solution, byusing a single electrochemical analytical cell and a single platingprotocol, comprising the steps of:

-   -   (a) selecting n compositional terms that include copper sulfate        concentration, sulfuric acid concentration, chloride ion        concentration, suppressor concentration, accelerator        concentration, leveler concentration, byproduct(s)        concentrations, and interactions between two or more of said        concentrations, wherein n≧3;    -   (b) establishing m multiple regression models that correspond to        m time points during the electrochemical metal deposition        process, wherein each model expresses electropotential responses        of electrochemical deposition solutions as a function of the n        selected compositional terms and their corresponding        coefficients, wherein m≧3;    -   (c) using said electrochemical analytical cell and said plating        protocol for measuring electropotential responses of multiple        calibration solutions at each of said m time points, wherein        said calibration solutions contain copper sulfate, sulfuric        acid, chloride ion, suppressor, accelerator, leveler, and/or        byproduct(s) at unique, known concentrations;    -   (d) determining the coefficients of said n selected        compositional terms for each of the m multiple regression        models, based on information obtained in step (c);    -   (e) using said electrochemical analytical cell and said plating        protocol for measuring electropotential responses of the sample        electrochemical deposition solution at each of said m time        points; and    -   (f) determining the n selected compositional terms based on the        established multiple regression models, the coefficients        determined in step (d), and the electropotential responses        measured in step (e); and    -   (g) calculating concentrations of copper sulfate, sulfuric acid,        chloride ion, suppressor, accelerator, leveler, and/or        byproduct(s) in the sample electrochemical deposition solution        from the compositional terms so determined.

Matrix inversion can be used for quickly and directly determining the nselected composition terms in step (f). Specifically, three matrixes X,β, and Y are constructed for representing the m multiple regressionmodels as Y=βX, wherein X is a n×1 compositional matrix containing the ncompositional terms, wherein β is a m×n coefficient matrix containingthe coefficients determined in step (d), and Y is a m×1 response matrixcontaining the electropotential responses measured in step (e). Thecompositional matrix X containing the n compositional terms can bedirected determined as X=(β′β)⁻¹β′Y, wherein β′ is the transpose of β,and wherein (β′β)⁻¹ is the inverse of β′β.

The time points used for establishing the multiple regression models canbe selected from any time instances during the electroplating process.For example, they can be selected from 0.2 second, 0.25 second, 0.5second, 1 second, 5 seconds, 10 seconds, and 20 seconds.

Other aspects, features and embodiments of the invention will be morefully apparent from the ensuing disclosure and appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a graph of multiple electropotential response curves measuredover time for a set of electrochemical deposition solutions containingorganic additives at different concentrations, wherein the measurementswere conducted with a potential pulse followed by current plating.

FIG. 1B is a graph of comparative electropotential response curvesmeasured for the same set of electrochemical deposition solutions as inFIG. 1A, wherein the measurements were conducted with a current pulsefollowed by current plating.

FIGS. 2A and 2B are illustrative potential waveforms during exemplarymeasurement cycles, according to two alternative embodiments of thepresent invention.

FIG. 3 is a plating transient measured for an electrochemical depositionsolution having 10% and 50% copper thiolate formation.

FIG. 4 is a plating transient for an aging electrochemical depositionsolution.

FIG. 5 is a plating transient for an aged electrochemical depositionsolution in a bleed and feed environment.

DETAILED DESCRIPTION AND PREFERRED EMBODIMENTS THEREOF

The present invention proposes various new electrochemical analyticalcell designs and new methodologies for conducting concentration analysisof electrochemical deposition (ECD) solutions, which are described indetail as follows. U.S. patent application Ser. No. 10/836,546 for“Methods and Apparatuses for Monitoring Organic Additives inElectrochemical Deposition Solutions” filed on Apr. 30, 2004 in the nameof Jianwen Han et al. is hereby incorporated by reference in itsentirety.

While the invention is described hereinafter in various embodimentsemploying copper ECD baths utilizing copper sulfate, sulfuric acid andchloride inorganic components, it will be recognized that the utility ofthe invention is not thus limited, but rather extends to and encompassesthe use of other salt, acid and anion inorganic components in ECD bathsfor copper deposition.

Electrochemical Deposition with an Initial Potential Pulse Followed byConstant Current

As described by U.S. Pat. Nos. 6,280,602; 6,459,011; 6,592,737; and6,709,568, a conventional PCGA measurement cycle that is useful forconcentration analysis of ECD solutions typically comprises thefollowing four steps:

-   -   (a) stripping, in which the copper layer previously deposited is        removed;    -   (b) cleaning, in which the measuring electrode surface is        thoroughly cleaned electrochemically or chemically using an acid        bath;    -   (c) equilibration (optional), in which the measuring electrode        and the reference electrode are exposed to the sample ECD        solution and allowed reach an equilibrium state; and    -   (d) plating, in which copper is electrochemically deposited onto        the measuring electrode under an initial current pulse followed        by a constant current, while the plating potential between the        measuring and counter electrodes is monitored and recorded.

One problem associated with such conventional PCGA method is that theplating potential signal is not stable during the plating step. As aresult, the determinations of organic additive concentrations are notsufficiently accurate for the high-precision control that is desiredfrom the perspective of high-volume manufacturing operations for thenext generation of semiconductors, in which reliable metrology iscritically important.

The present invention therefore provides a new PCGA method, based on thediscovery that use of a potential pulse, in place of a current pulse,followed by constant current plating during the plating step, yields aplating potential signal of significantly enhanced stability andaccuracy. Such enhancement of stability and accuracy in turn yieldsimproved measured results for organic additive, inorganic additiveand/or byproduct concentrations in operation of ECD baths.

Specifically, the potential pulse is applied for a sufficient period oftime to induce metal nucleation on the electrode surface, and preferablyfor duration of from about 1 microsecond to about 2.5 seconds. Forelectrochemical deposition of copper from a sample ECD solutioncomprising copper sulfate, sulfuric acid, chloride, and one or moreorganic additives, such potential pulse preferably has a magnitude offrom about −0.1V to about −1V, more preferably from about −0.1V to about−0.9V. Magnitude of such potential pulse can be readily modified by aperson ordinarily skilled in the art to adapt for electrochemicaldeposition of other metals or metal alloys using other ECD solutions.

For copper ECD, the constant current following such potential pulse ispreferably within a range of from about −1 mA/cm² to about −1000 mA/cm²,which can be readily modified by a person ordinarily skilled in the artfor adaptation to other types of ECD reactions using other ECDsolutions.

FIG. 1A shows the potential response curves of eight (8) differentcopper ECD solutions containing the suppressor, accelerator, and levelerat different, known concentrations (specified by Table I hereinafter),as measured under a 0.1 second potential pulse of about −0.7 V, followedby constant current plating at −100 mA/cm² for about 100 seconds. TABLEI Additive Concentration (ml/L) Solution Solution Solution SolutionSolution Solution Solution Solution #1 #2 #3 #4 #5 #6 #7 #8 Accelerator3 3 3 3 9 9 9 9 Leveler 1.25 1.25 3.75 3.75 1.25 1.25 3.75 3.75Suppressor 1 3 1 3 1 3 1 3

In comparison, FIG. 1B shows the potential response curves of the samesolutions #1-8, as measured under a 0.1 second current pulse of about−200 mA/cm², followed by constant current plating at −100 mA/cm² forabout 100 seconds.

It is evident that the potential response curves in FIG. 1A containlittle fluctuations over time and almost no overlapping between thecurves, while the potential response curves in FIG. 1B show significantfluctuations over time and overlapping therebetween.

Therefore, use of a potential pulse before constant current plating inthe plating process of the present invention provides plating potentialsignals of significantly enhanced stability and accuracy, in comparisonwith the conventional plating process that uses a current pulse beforethe constant current plating, and it constitutes an importantadvancement in the field of PCGA-based concentration analysis.

Electrochemical Concentration Analysis Using a Five-Step MeasurementCycle

A conventional measurement cycle useful for concentration analysis ofcopper ECD solutions typically comprises four steps, which include (1)stripping, (2) cleaning, (3) equilibrium, and (4) plating, as describedin U.S. Pat. Nos. 6,280,602; 6,459,011; 6,592,737; and 6,709,568.

The present invention provides a new measurement cycle that comprisesfive steps, including (1) initial stripping, (2) cyclic voltammetry (CV)scan cleaning, (3) equilibrium, (4) plating, and (5) post-platingstripping, for further reducing the risk of cross-contamination betweensample ECD solutions that are analyzed by sequentially by the sameelectrochemical analytical cell and further shortening the run timerequired for one measurement cycle.

Each steps of such new measurement cycle are described in detail in theensuring sections:

Electrostripping:

The new measurement cycle of the present invention starts withelectrostripping of the measuring electrode, which is carried out byapplying a positive potential (i.e., stripping potential) between themeasuring electrode and the counter electrode that is sufficient forelectrochemically removing the metal residue formed on the measuringelectrode during a previous measurement cycle.

When such measurement cycle is used for measuring sample ECD solutionsthat comprise copper sulfate, sulfuric acid, chloride, and optionallyone or more organic additives, the stripping potential is preferablywithin a range of from about 0.5V to about 1V, and more preferably fromabout 0.6V to about 0.8V. The duration of the electrostripping ispreferably from about 40 seconds to about 200 seconds and morepreferably from about 60 seconds to about 120 seconds. Electrostrippingat a stripping potential of less than 08V and for duration of at leasttwice of the plating duration (i.e., 2×) is particularly suitable forproducing reliable and stable measurement results.

An electrolytic cleaning solution containing sulfuric acid is preferablyused for conducting the electrostripping of the measuring electrode, byimmersing both the measuring and the counter electrodes in such cleaningsolution. More preferably, the measurement chamber containing themeasuring electrode and counter electrode is flushed with suchelectrolytic cleaning solution during the electrostripping. The flushingmay be carried out through the entire time of the electrostripping, orfor only a predetermined period of time (e.g., 10 seconds or 20seconds). In such manner, at least a portion of the metal residuestripped off the measuring electrode is carried out of the measurementchamber by the electrolytic cleaning solution, thereby reducing themetal concentration in the measurement chamber and reducing the risk ofmetal re-deposition onto the inner surfaces of the measurement chamberor counter electrode under the stripping potential.

CV Scan Cleaning:

The presence of surface-active organic materials, such as thesuppressor, accelerator, and leveler in the sample ECD solution leads toformation of an organic surface residual layer on the surface of themeasuring electrode, resulting in electrode passivation or a change inthe electrode surface state, and causing significant measurement errorsafter such measuring electrode is used for an extended period of time.Maintenance of a clean, reproducible electrode surface therefore is ofcritical importance in making meaningful electroanalytical measurements.

The present invention therefore provides a cyclic voltammetry-based (CVscan) cleaning step for removing the organic surface residue from themeasuring electrode, as well as the residue copper plated on the surfaceof the measuring electrode. CV scan is particularly effective for insitu cleaning and depassivating the electrode, with significantlyshortened system down time and reduced damages to the electrode surface.

Specifically, a cyclic electropotential is applied between the measuringelectrode and the counter electrode, while both electrodes are immersedin either a sample ECD solution or an electrolytic cleaning solution asdescribed hereinabove. Effective cleaning can be achieved by a cyclicelectropotential that oscillates between about −4V to about +4 v, morepreferably from about −1V to about +1V, and most preferably from about−0.7V to about 0.25V. Within such cycling range, the cyclicelectropotential oxidizes and/or reduces the organic surface residue andthe residue copper absorbed on the measuring electrode, thereforedepassivating the measuring electrode. Further, such cyclicelectropotential also generates multiple hydrogen and oxygenmicro-bubbles on the electrode surface within such cyclic range,therefore providing a vigorous surface process that functions to peelaway any non-oxidizable or non-reducible solid or liquid residues on theelectrode surface. CV scan results can also be used as an indicator ofthe cleanness of the surface of the measuring electrode. In the cathodicpotential scan range, four absorption/desorption hydrogen peaks shouldbe shown clearly if the measuring electrode surface is sufficientlyclean.

The scan rate (i.e., potential change rate) of the CV scan is preferablywithin the range of from about 0.1V/second to about 0.5V/second and morepreferably from about 0.2V/second to about 0.4V/second.

The CV scan duration is preferably at least 10 cycles, and morepreferably at least 15 cycles, and most preferably at least 20 cycles.

When the measurement cycle is used for measuring sample ECD solutionsthat comprise copper sulfate, sulfuric acid, chloride, and optionallyone or more organic additives, an electrolytic cleaning solutioncontaining sulfuric acid as described hereinabove is preferably used forconducting the CV scan cleaning step. More preferably, the measurementchamber containing the measuring electrode and counter electrode isflushed with such electrolytic cleaning solution during the CV scancleaning, so as to carry the organic surface residue out of themeasurement chamber and reduce cross-contamination thereby.

Equilibrium:

After the stripping and cleaning steps and before the actual plating,the measurement chamber is filled with a fresh sample ECD solution to beanalyzed, and the measuring and counter electrodes are both immersed insuch fresh sample ECD solution for a sufficient period of time until asteady state or an equilibrium state is reached.

Such equilibrium state can be reached either by disconnecting themeasuring electrode from the counter electrode to form an open circuitwith no electrical current passing therethrough, or by maintaining aclosed circuit while applying between the measuring and counterelectrodes a predetermined electropotential that is less than theplating potential required. In a specific embodiment of the presentapplication, a two-stage equilibrium is achieved by applying a potentialof from about −1V to about −0.1V during a first stage, and a potentialof from about 0.1V to about 1V during a second stage, wherein theduration of the first stage is at least twice longer than the secondstage. Preferably, during such first stage of the equilibrium, thesample ECD solution is continuously flushed through the measurementchamber.

Plating:

Metal electroplating in the present invention is preferable carried outat constant plating current, while the potential response of the sampleECD solution is concurrently monitored as an analytical signal fordetermining the organic additive, inorganic additive and/or byproductconcentrations in such sample solution.

Constant plating current within a range of from about −1 mA/cm² to about−1000 mA/cm², preferably from about −10 mA/cm² to about −500 mA/cm², issufficient for electrochemical metal deposition, and the platingduration is preferably from about 10 seconds to about 60 seconds, morepreferably from 10 seconds to about 30 seconds, and most preferably fromabout 15 seconds to about 25 seconds.

Preferably but not necessarily, the constant current plating is precededby a potential pulse of from about −0.1V to about −1V, which lasts onlyfrom about 1 microsecond to about 2.5 seconds. Such potential pulse isparticularly useful for optimizing metal nucleation on the electrodesurface and stabilizing the potential signals during the subsequentcurrent plating stage.

Post-Plating Stripping:

The metal deposition layer formed on the measuring electrode during theplating step, if not timely removed, may alloy with the metal componentof the measuring electrode, thereby deleteriously changing the surfacestate of the measuring electrode in an irreversible manner and causingsignificant measurement errors for future measurements.

Since the time interval between two adjacent measurement cycles may varysignificantly, it is important to ensure timely removal of such metaldeposition layer and avoid formation of alloy between such metaldeposition layer and the metal component of the measuring electrode.

The present invention therefore provides post-plating electrostrippingimmediately after the plating step, to remove at least a portion of themetal deposition layer before the commencement of the next measurementcycle. Therefore, prolonged time intervals between measurement cycleswill no longer cause surface state changes of the measuring electrode orreduce the measurement accuracy.

Such post-plating electrostripping can be carried out by applying apositive potential (i.e., the stripping potential) of from about 0.1V toabout 0.3V between the measuring electrode and the counter electrode forfrom about 20 seconds to about 60 seconds.

An electrolytic cleaning solution containing sulfuric acid is preferablyused for conducting the post-plating electrostripping. More preferably,the measurement chamber containing the measuring electrode and counterelectrode is flushed with such electrolytic cleaning solution, eitherthroughout the post-plating electrostripping step or for at least asufficient period of time (e.g., 20 to 40 seconds).

FIGS. 2A and 2B shows the potential waveforms for a two measurementcycle, according to two slightly different embodiments of the presentinvention.

Specifically, FIG. 2A shows a measurement cycle that comprises (1) aninitial electrostripping carried out in a sulfuric acid cleaningsolution at a stripping potential of about 0.7V for about 80-100seconds, during which the sulfuric acid cleaning solution flushes themeasurement chamber for about 10 seconds; (2) CV scan cleaning carriedout in a sulfuric acid cleaning solution at a cyclic potential thatoscillates between −0.7V to about 0.25V for about 20 cycles (i.e., n=20)with a scan rate of about 0.3V/second, throughout which the sulfuricacid cleaning solution continuously flushes the measurement chamber; (3)two-stage equilibrium carried out in a fresh sample ECD solution with aclose circuit between the measuring and counter electrodes, wherein afirst potential of about −0.7V is applied for about 80 seconds with thesample ECD solution continuously flushing through the measurementchamber during a first stage, and a second potential of about 0.82V isapplied for about 5 seconds in the sample ECD solution; (4)electroplating carried out in the sample ECD solution, by applying aninitial potential pulse of about −0.17V for about 0.141 seconds and asubsequent constant plating current of about −940 mA/cm² for about 20seconds, during which the potential responses of the sample ECD solutionis continuously monitored; and (5) post-plating electrostripping carriedout in a sulfuric acid cleaning solution at a stripping potential ofabout 0.3V for about 40 seconds, throughout which the sulfuric acidcontinuously flushes the measurement chamber.

FIG. 2B shows a measurement cycle similar to that illustrated in FIG.4A, except that the equilibrium is reached in an open circuit withoutsample flushing.

The entire runtime required for the measurement cycle of the presentinvention is not more than 20 minutes, and typically around 6-10minutes, which significantly increases the measurement efficiency andenables true real-time ECD bath analysis. Further, such measurementcycle further reduces the risk of cross-contamination between differentsample solutions analyzed by the same electrochemical analytical celland increases the accuracy of the measurement results.

Detection of Copper Thiolate Byproduct in Copper ECD Bath

The present invention provides a method for analyzing copper ECD bathbyproducts, such as copper thiolate, using the same analysis system usedto quantify organic and inorganic additives. Accordingly, another aspectof the inventions relates to methods of analyzing copper ECD bathcompositions comprising measuring ECD bath byproducts in addition toorganic additives and inorganic additives, and systems for performingsuch analysis. One preferred embodiment of the invention uses a singleanalysis system and/or a single sample. Most preferably, a single sampleof the bath composition is measured using a single analysis system.

Recently, it has been concluded that copper (I) thiolate species areformed through the redox reaction of Cu⁺ with the accelerator additivebis(sodiumsulfopropyl) disulfide (SPS) (Vereecken, P. M., Binstead, R.A., Deligianni, H., Andricacos, P. C., IBM J. Res. & Dev., 49(1), 3-18(2005)). It is well recognized in the ECD art that the byproduct copperthiolate may play a role in accelerating copper deposition duringdamascene plating (Healy, J. P., Pletcher, D., Goodenough, M., J.Electroanalyt. Chem., 338, 167-177 (1992); Healy, J. P., Pletcher, D.,Goodenough, M., J. Electroanalyt. Chem., 338, 179-187 (1992); Kim, J.J., Kim, S.-K., Kim, Y. S., J. Electroanalyt. Chem., 542, 61-66 (2003).

Given its role as an accelerator in the copper ECD bath, the copperthiolate byproduct is preferably monitored with the intent ofcontrolling the overall concentration of said byproduct. For example,using a bleed and feed environment, when the concentration of copperthiolate becomes too great, some of the bulk ECD bath may be bled offand fresh chemistries introduced.

We have unexpectedly discovered that copper thiolate may be monitoredand quantified using the same analysis system used to quantify organicand inorganic additives.

A copper ECD bath including copper sulfate, sulfuric acid, chloride ion,leveler (1.5 mL L⁻¹), suppressor (2 mL L⁻¹) and accelerator (6 mL L⁻¹)was prepared and an electrochemical concentration analysis using thefive-step measurement cycle described herein was performed at constantcurrent. A Defect Analysis Reduction Tool (DART) plating transient wasobtained, which provides information on the electrode interface as wellas a reflection of what species are present in the bulk solution. TheDART plating transient shown in FIG. 3 shows that when just 10% of theSPS accelerator converted into byproduct, and the change in potential ofthe ECD bath was quantifiable Clearly, the breakdown product copperthiolate is very easy to distinguish in a fresh ECD bath.

Thereafter, aged baths were monitored to determine the effect of thecopper thiolate byproduct on the DART plating transient. Referring toFIG. 4, it can be seen that aged ECD baths continued to acceleratethrough 4, 8 and 12 Amp-hr L⁻¹. Importantly, the shape of the transientsin FIGS. 3 and 4 essentially mimic one another, which supports thatnotion that copper thiolate or similar species are the primary byproductover time.

FIG. 5 represents the measurement of copper thiolate byproduct in ableed and feed environment, using both fresh chemistries as well as agedchemistries. The target ECD bath solution included 9 mL L⁻¹ accelerator,2 mL L⁻¹ suppressor, 1.5 mL L⁻¹ leveler and zero copper thiolatebyproduct. After aging for 4 Amp-hr L⁻¹, with no additional dose ofaccelerator, the concentration of accelerator decreased to 7.9 mL L⁻¹,while the percent byproduct was 25%. In contrast, a 4 Amp-hr L⁻¹ agedbath with a dose of 1.5 mL L⁻¹ accelerator, had a concentration ofaccelerator of 10.7 mL L⁻¹ and a percent byproduct of 12.6%.Importantly, it is possible to quantify the acceleration differencesassociated with aging (and hence copper thiolate production) and theaddition of fresh accelerator chemistries.

In conclusion, the present inventors have shown that the copper thiolatebyproduct may be monitored and quantified using the same analysis systemused to quantify organic and inorganic additives. Furthermore, theexistence of the byproduct species may be monitored in aged ECD baths.

Concentration Analysis Based on a Single Multiple Regression Model

The present invention provides a method for simultaneously determiningthe concentrations of multiple organic additives, e.g., suppressor,accelerator, and leveler, multiple inorganic additives, e.g., coppersulfate, sulfuric acid, chloride ion, and/or byproducts (e.g., copperthiolate) thereof, in a sample ECD solution, based on a single multipleregression model that defines the electroplating potential of the samplesolution as a function of multiple variables that represent both thecompositional parameters, such as the additive concentrations, as wellas non-compositional parameters associated with the measurement cycle.

First, various non-compositional variables that may have potentialimpacts on the electroplating potential of the sample ECD solution aretested for their respective significance with respect to theelectroplating potential. Specifically, electroplating potentials of oneor more sample ECD solutions under varying values of the potentialnon-compositional variables are measured to establish a sample data setfor analysis of variance tests, in which the estimated coefficient(i.e., parameter) of each non-compositional variable and the probabilitythat such coefficient may equal zero are determined. Thenon-compositional variables having non-zero coefficients at confidencelevels above a predetermined threshold (for example, not less than 95%,which means that the probability that the coefficients of such variablesare not zero is equal to or more than 95%) are selected.

By testing various non-compositional variables, nucleation potential,nucleation time, electroplating current, electroplating time, with orwithout CV scan cleaning, scan rate of the CV scan, types of cleaningsolution used, size of the measuring electrode used, sample solutionde-aeration, and equilibrium time have been found to have impact on theelectroplating potential. Particularly, the nucleation potential, thenucleation time, the electroplating current, the electroplating time,the CV scan duration, and the size of the measuring electrode influencehave significant impact on the plating potential.

A multiple regression model can therefore be established to express theelectropotential responses of ECD solutions as a function of one or moreabove-described non-compositional variables, the organic additivesconcentrations, the inorganic additives concentrations, the byproduct(s)concentration(s) and their corresponding coefficients.

Preferably, one or more terms representing the interactions between theorganic additive, inorganic additive and/or byproduct concentrations andthe non-compositional variables are included in such multiple regressionmodel. Quadratic terms and/or cubic terms can also be included.

For illustration purposes while without limiting the broad scope of thepresent application, an exemplary multiple regression model isestablished as follows:Y=β ₀+β₁ ×A+β ₂ ×B+β ₃ ×C+β ₄ ×D+β ₅ ×E+β ₆ ×Acc+β ₇ ×Lev+β ₈ ×Supp+β ₉×Cop+β ₁₀ ×Sul+β ₁₁ ×Chl+β ₁₂ ×Byp+β ₁₃ ×A ²+β₁₄ ×AC+β ₁₅ ×AE+β ₁₆×A×Acc+β ₁₇ ×B ²+β₁₈ ×BD+β ₁₉ ×C ²+β₂₀ ×CE+β ₂₁ ×C×Lev+β ₂₂ ×D ²+β₂₃ ×E²β₂₄ ×AE×Lev+β ₂₅ ×AE×Supwherein Y is the electroplating potential measured for a sample ECDsolution; A is the nucleation potential (V); B is the nucleation time(second); C is the electroplating current (mA/cm²); D is the CV scanduration (second); E is the size of the measuring electrode (μm); Acc isthe concentration of the accelerator in the ECD solution; Lev is theconcentration of the leveler; Sup is the concentration of thesuppressor; Cop is the concentration of the copper sulfate in the ECDsolution; Sul is the concentration of the sulfuric acid in the ECDsolution; Chl is the concentration of the chloride ion in the ECDsolution; Byp is the concentration of the byproduct in the ECD solution;AC, AE, BD, and CE represent two-way interactions between thenon-compositional variables ABCDE; A×Acc and C×Lev represent two-wayinteractions between a non-compositional variable and an additiveconcentration; AE×Lev and AE×Sup represent three way interactionsbetween two non-compositional variables and an additive concentration;A², B², C², D², and E² are the quadratic terms of the non-compositionalvariables ABCDE; β₀ is the intercept; and β₁-β₂₅ are the coefficientsfor all the terms of the multiple regression model. Other two-way andthree-way interactions (with coefficients), as readily determined by oneskilled in the art, may be incorporated into the exemplary regressionmodel. In addition, more or less additives and/or byproducts may beincorporated into the model. Thus, more or less coefficients, i.e., β,may be necessary.

The intercept β₀ and the coefficients β₁-β₂₅ of the above multipleregression model can be readily determined by running multiplecalibration measurements, each of which measures the electroplatingpotential of a calibration solution containing copper sulfate, sulfuricacid, chloride ion, the suppressor, the accelerator, the leveler, and/orthe byproduct(s) at known concentrations at predetermined measurementsettings, i.e., with predetermined values of the non-compositionalvariables A, B, C, D, and E.

Subsequently, N experimental runs are designed for measuring the sampleECD solution containing the organic additives, inorganic additivesand/or byproduct(s) at unknown concentrations. Each experimental run ischaracterized by a unique, predetermined measurement setting, i.e., withpredetermined values of the non-compositional variables A, B, C, D, andE. As defined herein, “N” corresponds to the total number of speciesbeing quantified, wherein the species may include organic additives,inorganic additives, and/or byproducts thereof. For example, asincorporated into the multiple regression model hereinabove, sevenspecies may be quantified simultaneously, including copper sulfate,sulfuric acid, chloride ion, leveler, accelerator, suppressor, andcopper thiolate (byproduct). It should be appreciated that more or lessspecies are simultaneously quantifiable.

The electroplating potentials of the sample ECD solution are thenmeasured for these N experimental runs, to establish N equations, asfollows:Y _(N)=β₀+β₁ ×A _(N)+β₂ ×B _(N)+β₃ ×C _(N)+β₄ ×D _(N)+β₅ ×E _(N)+β₆×Acc+β ₇ ×Lev+β ₈ ×Sup+β ₉ ×Cop+β ₁₀ ×Sul+β ₁₁ ×Chl+β ₁₂ ×Byp+β ₁₃ ×A_(N) ²+β₁₄ ×A _(N) C _(N)+β₁₅ ×A _(N) E _(N)+β₁₆ ×A _(N) ×Acc+β ₁₇ ×B_(N) ²+β₁₈ ×B _(N) D _(N)+β₁₉ ×C _(N) ²+β₂₀ ×C _(N) E _(N)+β₂₁ ×C _(N)×Lev+β ₂₂ ×D _(N) ²+β₂₃ ×E _(N) ²+β₂₄ ×A _(N) E _(N) ×Lev+β ₂₅ ×A _(N) E_(N) ×Supwherein Y_(N) corresponds to the electroplating potentials of the sampleECD solution as measured during the N experimental runs, whereinA_(N)-E_(N) are the respective predetermined values of thenon-compositional variables ABCDE during the N experimental runs.

Therefore, N equations contain only N unknown values. Such unknownconcentration values can thus be readily determined by solving Nequations.

The N experimental runs can be carried out sequentially in the sameelectrochemical analytical cell. Alternatively, they can be carried outsimultaneously in N electrochemical analytical cells, each of whichoperates according to a unique, predetermined measurement protocol withpredetermined values for the non-compositional variables ABCDE.

The number and type of non-compositional variables to be included intothe multiple regression model can be readily modified by a personordinarily skilled in the art. The essence of this invention is to use Nexperimental runs to provide N equations with only N unknown valuescorresponding to the additive and/or byproduct concentrations, which arereadily solvable for concentration determination. Therefore, as few asone non-compositional variable and as many as infinite number ofvariables can be included into the model. When more variables areincluded, the model is more sophisticated and provides more accurateanalytical results.

Concentration Analysis Using a Single Experimental Run

The present invention provide another method for simultaneouslydetermining concentrations of organic additive (e.g., accelerator,leveler, and suppressor), inorganic additive (e.g., copper sulfate,sulfuric acid, chloride ion) and/or byproduct(s) (e.g., copper thiolate)in a sample ECD solution within a single experimental run, wherein timeis used as a variable for constructing three or more multiple regressionmodels, and wherein interactions between the additives and/orbyproduct(s) are accounted for.

This method, unlike the method described in the previous section, doesnot rely on usage of any non-compositional variables associated with theexperimental settings. Instead, it considers only compositional termsassociated with the additive and/or byproduct(s) concentrations and theinteractions therebetween.

The concentrations of copper sulfate, sulfuric acid, chloride ion,accelerator, leveler, suppressor, and/or byproduct(s) are the basic andnecessary compositional variables to be included. Additionalcompositional terms representing interactions between the additives,byproduct(s) or quadratic/cubic terms may also be included. For example,additional compositional terms have potential impacts on theelectroplating potential of the sample ECD solution can be tested fortheir respective significance with respect to the electroplatingpotential. Specifically, electroplating potentials of one or more sampleECD solutions under varying values of such additional compositionalterms are measured to establish a sample data set for analysis ofvariance tests, in which the estimated coefficient (i.e., parameter) ofeach additional compositional term and the probability that suchcoefficient may equal zero are determined. The additional compositionalterms having non-zero coefficients at confidence levels above apredetermined threshold (for example, not less than 95%, which meansthat the probability that the coefficients of such variables are notzero is equal to or more than 95%) can be selected for inclusion.

For illustrative purposes, the following compositional terms can beselected, which include: A Accelerator concentration B Levelerconcentration C Suppressor concentration D Copper sulfate concentrationE Sulfuric acid concentration F Chloride ion concentration G Byproductconcentration AB Interaction between accelerator and leveler ACInteraction between accelerator and suppressor ABC Interaction betweenaccelerator, leveler, and suppressor AA Quadratic term for acceleratorBB Quadratic term for leveler CC Quadratic term for suppressor DDQuadratic term for copper sulfate EE Quadratic term for sulfuric acid FFQuadratic term for chloride ion GG Quadratic term for byproduct

Other compositional interactions are readily determined by one skilledin the art and may be incorporated into the multiple regression modelsherein. In addition, more or less additives and/or byproducts may beincorporated into said models.

The selected compositional terms can then be used to establish mmultiple regression models that corresponds to m time points (t₁, t₂, .. . t_(m)) during the electrochemical metal deposition process, whereineach model expresses electropotential responses of the ECD solutions asa function of the selected compositional terms and their correspondingcoefficients, wherein m≧3.

For example, three multiple regression models that correspond to threetime points (t₁, t₂, and t₃) can be established, as follows:Y ₁=β_(A) ¹ ×A+β _(B) ¹ ×B+β _(C) ¹ ×C+β _(D) ¹ ×D+β _(E) ¹ ×E+β _(F) ¹×F+β _(G) ¹ ×G+β _(AB) ¹ ×AB+β _(AC) ¹ ×AC+β _(ABC) ¹ ×ABC+β _(AA) ¹×AA+β _(BB) ¹ ×BB+β _(CC) ¹ ×CC+β _(DD) ¹ ×DD+β _(EE) ¹ ×EE+β _(FF) ¹×FF+β _(GG) ¹ ×GGY ₂=β_(A) ² ×A+β _(B) ² ×B+β _(C) ² ×C+β _(D) ² ×D+β _(E) ² ×E+β _(F) ²×F+β _(G) ² ×G+β _(AB) ² ×AB+β _(AC) ² ×AC+β _(ABC) ² ×ABC+β _(AA) ²×AA+β _(BB) ² ×BB+β _(CC) ² ×CC+β _(DD) ² ×DD+β _(EE) ² ×EE+β _(FF) ²×FF+β _(GG) ² ×GGY ₃=β_(A) ³ ×A+β _(B) ³ ×B+β _(C) ³ ×C+β _(D) ³ ×D+β _(E) ³ ×E+β _(F) ³×F+β _(G) ³ ×G+β _(AB) ³ ×AB+β _(AC) ³ ×AC+β _(ABC) ³ ×ABC+β _(AA) ³×AA+β _(BB) ³ ×BB+β _(CC) ³ ×CC+β _(DD) ³ ×DD+β _(EE) ³ ×EE+β _(FF) ³×FF+β _(GG) ³ ×GGwherein Y₁, Y₂, and Y₃ are the electroplating potentials measured atrespective time points t₁, t₂, and t₃; β_(A) ¹-β_(GG) ¹ are thecoefficients for the selected compositional terms A-GG at time point t₁;β_(A) ²-β_(GG) ² are the coefficients for the selected compositionalterms A-GG at time point t₂; β_(A) ³-β_(GG) ³ are the coefficients forthe selected compositional terms A-GG at time point t₃.

The values of the coefficients β_(A) ¹-β_(GG) ¹, β_(A) ²-β_(GG) ², andβ_(A) ³-β_(GG) ³ can be readily determined by running multiplecalibration measurements of various calibration solutions having unique,known organic additive, inorganic additive, and/or byproductconcentrations, and during each calibration measurement, theelectroplating potential is measured three times, at each of the timepoints t₁, t₂, and t₃.

Subsequently, a single experimental run is carried out for measurementof the sample ECD solution that contains the additives and/orbyproduct(s) at unknown concentrations. Electroplating potentials ofsuch sample ECD solution at the three time points t₁, t₂, and t₃ aresequentially measured during the experimental run and recorded as Y₁,Y₂, and Y₃.

Based on the three multiple regression models established hereinabove,the coefficient values determined via calibration measurements, and theelectroplating potentials measured during the experimental run, one canreadily calculating the organic additive concentrations A, B, and C, theinorganic concentrations D, E, and F, and the byproduct concentration G.

A quick and direct method for calculating the additive and/orbyproduct(s) concentrations relies on matrix inversion. Specifically,three matrices X, β, and Y are constructed as follows:$X = \begin{pmatrix}A \\B \\C \\D \\E \\F \\G \\{AB} \\{A\quad C} \\{ABC} \\{AA} \\{BB} \\{CC} \\{DD} \\{EE} \\{FF} \\{GG}\end{pmatrix}$ $B = \begin{pmatrix}\beta_{A}^{1} & \beta_{B}^{1} & \beta_{C}^{1} & \beta_{D}^{1} & \beta_{E}^{1} & \beta_{F}^{1} & \beta_{G}^{1} & \beta_{AB}^{1} & \beta_{A\quad C}^{1} & \beta_{ABC}^{1} & \beta_{AA}^{1} & \beta_{BB}^{1} & \beta_{CC}^{1} & \beta_{DD}^{1} & \beta_{EE}^{1} & \beta_{FF}^{1} & \beta_{GG}^{1} \\\beta_{A}^{2} & \beta_{B}^{2} & \beta_{C}^{2} & \beta_{D}^{2} & \beta_{E}^{2} & \beta_{F}^{2} & \beta_{G}^{2} & \beta_{AB}^{2} & \beta_{A\quad C}^{2} & \beta_{ABC}^{2} & \beta_{AA}^{2} & \beta_{BB}^{2} & \beta_{CC}^{2} & \beta_{DD}^{2} & \beta_{EE}^{2} & \beta_{FF}^{2} & \beta_{GG}^{2} \\\beta_{A}^{3} & \beta_{B}^{3} & \beta_{C}^{3} & \beta_{D}^{3} & \beta_{E}^{3} & \beta_{F}^{3} & \beta_{G}^{3} & \beta_{AB}^{3} & \beta_{A\quad C}^{3} & \beta_{ABC}^{3} & \beta_{AA}^{3} & \beta_{BB}^{3} & \beta_{CC}^{3} & \beta_{DD}^{3} & \beta_{EE}^{3} & \beta_{FF}^{3} & \beta_{GG}^{3}\end{pmatrix}$ $Y = \begin{pmatrix}Y_{1} \\Y_{2} \\Y_{3}\end{pmatrix}$

The three multiple regression models as described herein above can berepresented by a simple matrix-based model that defines Y=βX, wherein Xis a compositional matrix containing the selected compositional terms,wherein β is a coefficient matrix containing the coefficients determinedvia calibration measurements, and Y is a response matrix containing theelectropotential responses measured via experimental run.

Since both matrices β and Y contain known elements (i.e., β_(A) ¹-β_(CC)¹, β_(A) ²-β_(CC) ², β_(A) ³-β_(CC) ³, and Y₁-Y₂), they can be used todetermined the unknown elements (i.e., A, B, C, . . . GG) contained inmatrix X.

From βX=Y, the following can be obtained:(β′β)X=Yβ′(β′β)⁻¹(β′β)X=Yβ′(β′β)⁻¹wherein β′ is the transpose of β, and wherein (β′β)⁻¹ is the inverse ofβ′β.

Since (β′β)⁻¹(β′β) equals the identity matrix I, and since the productof identity matrix I with any matrix A will still be A, we can derive Xas:X=Yβ′(β′β)⁻¹

When β is known, its transpose, β′, and the inverse of their product(β′β)⁻¹ can be readily calculated. Therefore, the concentrations of theorganic additives (A, B, and C), inorganic additives (D, E, and F)and/or byproduct(s) (G) can be directly determined as the elements ofthe matrix X.

The above example uses seventeen compositional terms and three multipleregression models for simplicity. In practice, the number ofcompositional terms can be more or less than seventeen (but not lessthan three), while more than three multiple regression models can beused.

In general, n compositional terms can be selected to establish mmultiple regression models (n≧3, and m≧3), as follows:Y ₁=β₁₁ ×X ₁+β₁₂ ×X ₂+β₁₃ ×X ₃+ . . . β_(1n) ×X _(n)Y ₂=β₂₁ ×X ₁+β₂₂ ×X ₂+β₂₃ ×X ₃+ . . . +β_(2n) ×X _(n)Y ₃=β₃₁ ×X ₁+β₃₂ ×X ₂+β₃₃ ×X ₃+ . . . +β_(3n) ×X _(n)Y _(m)=β_(m1) ×X ₁+β_(m2) ×X ₂+β_(m3) ×X ₃+ . . . +β_(mn) ×X _(n)wherein X₁, X₂, X₃, . . . , X_(n) are the n selected compositionalterms; Y₁, Y₂, Y₃, . . . , Y_(m) are the electroplating potentialsmeasured at m time points t₁, t₂, t₃, . . . , t_(m); β₁₁-β_(1n) are thecoefficients for the selected compositional terms X₁-X_(n) at time pointt₁; β₂₁-β_(2n) are the coefficients for the selected compositional termsX₁-X_(n) at time point t₂; β₃₁-β_(3n) are the coefficients for theselected compositional terms X₁-X_(n) at time point t₃; . . . ; andβ_(m1)-β_(mn) are the coefficients for the selected compositional termsX₁-X_(n) at time point t_(m).

The three matrices X, β, and Y can then be constructed as follows:$X = \begin{pmatrix}X_{1} \\X_{2} \\X_{3} \\\ldots \\X_{n}\end{pmatrix}$ $B = \begin{pmatrix}\beta_{11} & \beta_{12} & \beta_{13} & \ldots & \beta_{1n} \\\beta_{21} & \beta_{22} & \beta_{23} & \ldots & \beta_{2n} \\\beta_{31} & \beta_{32} & \beta_{33} & \ldots & \beta_{3n} \\\ldots & \ldots & \ldots & \ldots & \ldots \\\beta_{m\quad 1} & \beta_{m\quad 2} & \beta_{m\quad 3} & \ldots & \beta_{m\quad n}\end{pmatrix}$ $Y = \begin{pmatrix}Y_{1} \\Y_{2} \\Y_{3} \\\ldots \\Y_{m}\end{pmatrix}$

As shown, the generalized compositional matrix X is a n×1 matrixcontaining the n compositional terms; the generalized coefficient matrixβ is a m×n matrix; and the generalized response matrix Y is a m×1matrix.

Various time points during the electrochemical deposition process can beselected for constructing the multiple regression models. For example,for constructing the three multiple regression models as illustratedhereinabove, the time points at 5 seconds, 10 seconds, and 20 secondscan be used, while additional time points at 0.2 second, 0.25 second,0.5 second, and 1 second can also be used.

While the ensuing description of the invention contains reference toillustrative embodiments and features, it will be recognized that themethodology and apparatus of the invention are not thus limited, butrather generally extend to and encompass the determination of analytesin fluid media. For example, although the present description isdirected primarily to copper ECD deposition analysis, the invention isreadily applicable to other ECD processes, including deposition ofsilver, gold, iridium, palladium, tantalum, titanium, chromium, cobalt,tungsten, etc., as well as deposition of alloys and deposition ofamalgams such as solder. Examples of additional applications of theinvention other than ECD plating of semiconductor device structuresinclude analysis of reagents in reaction media for production oftherapeutic agents such as pharmaceutical products, and biotechnologyapplications involving the concentrations of specific analytes in humanblood or plasma. It will therefore be appreciated that the invention isof broad application, and that the ECD system and method describedhereafter is but one of a myriad of potential uses for which theinvention may be employed.

1. A method for simultaneously determining concentrations of coppersulfate, sulfuric acid, chloride ion, suppressor, accelerator, leveler,and/or byproduct(s) thereof in a sample electrochemical depositionsolution, comprising the steps of: (a) identifying one or morenon-compositional variables that affect electropotential responses ofelectrochemical deposition solutions during electrochemical metaldeposition; (b) establishing a multiple regression model that expressesthe electropotential responses of electrochemical deposition solutionsas a function of (1) said one or more non-compositional variables, (2)organic additive concentrations in the solutions, (3) inorganic additiveconcentrations in the solutions, (4) byproduct concentrations in thesolutions, and the corresponding coefficients; (c) conducting multiplecalibration runs, by measuring electropotential responses of multiplecalibration solutions having unique, known organic additive, inorganicadditive, and/or byproduct concentrations at unique, predeterminedvalues of said one or more variables; (d) determining the coefficientsthat correspond to said one or more variables and the organic additive,inorganic additive, and/or byproduct concentrations in the multipleregression model, based on information obtained from the calibrationruns; and (e) conducting N experimental runs, by measuringelectropotential responses of the sample electrochemical depositionsolution at unique, predetermined values of said one or more variables;(f) establishing N number of equations based on the established multipleregression model, said equations containing the coefficients determinedin step (d), the electropotential responses measured during the Nexperimental runs in step (e) and the corresponding predetermined valuesof said one or more variables, and the unknown concentrations of thecopper sulfate, sulfuric acid, chloride ion, suppressor, accelerator,leveler, and/or byproduct(s) thereof in the sample electrochemicaldeposition solution; and (g) calculating said copper sulfate, sulfuricacid, chloride ion, suppressor, accelerator, leveler, and/or byproductconcentrations in the sample solution by solving the N equationsprovided in step (f).
 2. The method of claim 1, wherein said one or morenon-compositional variables are identified by conducting analysis ofvariance tests on all non-compositional variables having potentialimpact on electropotential responses of electrochemical depositionsolutions and selecting those variables having non-zero coefficients atconfidence levels that are not less than 95%.
 3. The method of claim 1,wherein said one or more non-compositional variables are selected fromthe group consisting of (1) nucleation potential, (2) nucleation time,(3) electroplating current, (4) electroplating time, (5) scan rate ofthe cyclic voltammetry during pre-plating cleaning process, and (6) sizeof the measuring electrode used for conducting the electrochemical metaldeposition.
 4. The method of claim 1, wherein said multiple regressionmodel includes terms that account for interactions (1) between saidnon-compositional variables, (2) between the organic additiveconcentrations, (3) between the inorganic additives, (4) between thebyproduct(s) and/or (5) between one or more non-compositional variablesand one or more organic additive, inorganic additive, and/or byproductconcentrations.
 5. The method of claim 1, wherein in step (e), said Nexperimental runs are conducted in N different electrochemicalanalytical cells, wherein each cell performs electropotentialmeasurements on the sample electrochemical deposition solution accordingto a unique, predetermined plating protocol.
 6. The method of claim 5,wherein each plating protocol differs from the other two by at least onefactor selected from the group consisting of (1) nucleation potential,(2) nucleation time, (3) electroplating current, (4) electroplatingtime, (5) scan rate of the cyclic voltammetry during pre-platingcleaning process, and (6) size of the measuring electrode used forconducting the electrochemical metal deposition.
 7. The method of claim1, wherein N is in a range from about 3 to about
 10. 8. The method ofclaim 1, wherein N is
 7. 9. The method of claim 1, wherein the byproductcomprises copper (I) thiolate.
 10. A method for simultaneouslydetermining concentrations of copper sulfate, sulfuric acid, chlorideion, suppressor, accelerator, leveler, and/or byproduct(s) thereof in asample electrochemical deposition solution, by using a singleelectrochemical analytical cell and a single plating protocol,comprising the steps of: (a) selecting n compositional terms thatinclude copper sulfate concentration, sulfuric acid concentration,chloride ion concentration, suppressor concentration, acceleratorconcentration, leveler concentration, byproduct(s) concentrations, andinteractions between two or more of said concentrations, wherein n≧3;(b) establishing m multiple regression models that correspond to m timepoints during the electrochemical metal deposition process, wherein eachmodel expresses electropotential responses of electrochemical depositionsolutions as a function of the n selected compositional terms and theircorresponding coefficients, wherein m≧3; (c) using said electrochemicalanalytical cell and said plating protocol for measuring electropotentialresponses of multiple calibration solutions at each of said m timepoints, wherein said calibration solutions contain copper sulfate,sulfuric acid, chloride ion, suppressor, accelerator, leveler, and/orbyproduct(s) at unique, known concentrations; (d) determining thecoefficients of said n selected compositional terms for each of the mmultiple regression models, based on information obtained in step (c);(e) using said electrochemical analytical cell and said plating protocolfor measuring electropotential responses of the sample electrochemicaldeposition solution at each of said m time points; and (f) determiningthe n selected compositional terms based on the established multipleregression models, the coefficients determined in step (d), and theelectropotential responses measured in step (e); and (g) calculatingconcentrations of copper sulfate, sulfuric acid, chloride ion,suppressor, accelerator, leveler, and/or byproduct(s) in the sampleelectrochemical deposition solution from the compositional terms sodetermined.
 11. The method of claim 10, wherein in step (f), the nselected compositional terms are determined by: (i) establishing threematrices X, β, and Y to represent the m multiple regression models asY=βX, wherein X is a n×1 compositional matrix containing the ncompositional terms, wherein β is a m×n coefficient matrix containingthe coefficients determined in step (d), and Y is a m×1 response matrixcontaining the electropotential responses measured in step (e); and (ii)determining the compositional matrix X as:X=(β′β)⁻¹ β′Y wherein β′ is the transpose of β, and wherein (β′β)⁻¹ isthe inverse of β′β.
 12. The method of claim 10, wherein saidcompositional terms are selected by conducting analysis of variancetests on all linear, quadratic, and cubic terms related to the coppersulfate, sulfuric acid, chloride ion, suppressor, accelerator, leveler,byproduct(s) concentrations and interactions therebetween regardingtheir potential impact on electropotential responses of electrochemicaldeposition solutions, and selecting those terms having non-zerocoefficients at confidence levels that are not less than 95%.
 13. Themethod of claim 10, wherein 3 multiple regression models correspondingto 3 time points during the electrochemical metal deposition process areestablished.
 14. The method of claim 13, wherein said three time pointsare selected from the group consisting of 0.2 second, 0.25 second, 0.5second, 1 second, 5 seconds, 10 seconds, and seconds, as measured fromthe initiation of the electrochemical metal deposition process.
 15. Themethod of claim 10, wherein the byproduct comprises copper (I) thiolate.16. A method for simultaneously determining concentrations of inorganicadditives, suppressor, accelerator, leveler, and/or byproduct(s) thereofin a sample electrochemical deposition solution, comprising the stepsof: (a) identifying one or more non-compositional variables that affectelectropotential responses of electrochemical deposition solutionsduring electrochemical metal deposition; (b) establishing a multipleregression model that expresses the electropotential responses ofelectrochemical deposition solutions as a function of (1) said one ormore non-compositional variables, (2) organic additive concentrations inthe solutions, (3) inorganic additive concentrations in the solutions,(4) byproduct concentrations in the solutions, and the correspondingcoefficients; (c) conducting multiple calibration runs, by measuringelectropotential responses of multiple calibration solutions havingunique, known organic additive, inorganic additive, and/or byproductconcentrations at unique, predetermined values of said one or morevariables; (d) determining the coefficients that correspond to said oneor more variables and the organic additive, inorganic additive, and/orbyproduct concentrations in the multiple regression model, based oninformation obtained from the calibration runs; and (e) conducting Nexperimental runs, by measuring electropotential responses of the sampleelectrochemical deposition solution at unique, predetermined values ofsaid one or more variables; (f) establishing N number of equations basedon the established multiple regression model, said equations containingthe coefficients determined in step (d), the electropotential responsesmeasured during the N experimental runs in step (e) and thecorresponding predetermined values of said one or more variables, andthe unknown concentrations of the inorganic additives, suppressor,accelerator, leveler, and/or byproduct(s) thereof in the sampleelectrochemical deposition solution; and (g) calculating said inorganicadditives, suppressor, accelerator, leveler, and/or byproductconcentrations in the sample solution by solving the N equationsprovided in step (f).
 17. The method of claim 16, wherein the inorganicadditives comprise a copper salt.
 18. The method of claim 16, whereinthe inorganic additives comprise copper sulfate.
 19. The method of claim16, wherein the inorganic additives comprise sulfuric acid.
 20. Themethod of claim 16, wherein the inorganic additives comprise chlorideion.